反证法在证题中的应用

Reduction to Absurdity in Working Out Problems

反证法是数学教学中所涉及的基本论证方法,它为一些从正面入手,无法使已知条件和结论找出联系的问题,提供了一条解题途径。它是通过给出合理的反设,来增加演绎推理的前提,从而使那种只依靠所给前提而变得山穷水尽的局面,有了柳岸花明又一村的境地,使学生看到增加演绎推理前提的方便功效。

Reduction to absurdity is one of the principal proving methods involved in mathematics teaching. It provides a solution to the problems in which we couldn't find out the relationship between the given conditions and the conclusion only through the general steps. If we provide the prerequistes to the question in deduction and inference through reasonable counter-hypothesis the situation on the horns of a dilemma caused by only depending on prerequisites will have got a bright transition and the students will see the convenience and efficiency of attaching importance to deductive reasoning in mathematics learning.